PATTERN MATCHING PROBABILITIES AND PARADOXES AS A NEW VARIATION ON PENNEY'S COIN GAME
Yutaka Nishiyama · 2010
Abstract: This paper gives an outline of an interesting probability game related to coin arrangements discovered by Walter Penney in 1969, and explains John Conway’s concept of leading numbers and his algorithm for using them to automatically calculate mutual odds of winning. I will show that Conway’s elegant algorithm is correct by using average waiting times as proposed by Stanley Collings, and discuss the effect of applying the rules of this coin game to a card game instead.